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## Homework Statement

This isn't a homework question, just something I've been thinking about. If given a situation in which mass m is hung on a spring with constant k, I know you can set the spring force equal to the weight of the mass to find how far it stretches. Is there a way to find how far it stretches using energy equations? It seems like it should be doable, but I can't figure out how.

## Homework Equations

w = mg

F = -kx

ΔU

_{g}= mgh

U

_{s}= kx

^{2}/2

## The Attempt at a Solution

As I said, setting mg = kx can solve for x. How do I do it with energy though?

U

_{g}= U

_{s}

mgx = kx

^{2}/2

But now I get a different answer for x. What did I do wrong with the energy equations?